US8384588B2  Beam stabilization for wideband phase comparison monopulse angle estimation with electronically steered antennas  Google Patents
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 US8384588B2 US8384588B2 US12/925,668 US92566810A US8384588B2 US 8384588 B2 US8384588 B2 US 8384588B2 US 92566810 A US92566810 A US 92566810A US 8384588 B2 US8384588 B2 US 8384588B2
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 G—PHYSICS
 G01—MEASURING; TESTING
 G01S—RADIO DIRECTIONFINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCEDETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
 G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
 G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
 G01S13/06—Systems determining position data of a target
 G01S13/42—Simultaneous measurement of distance and other coordinates
 G01S13/44—Monopulse radar, i.e. simultaneous lobing
 G01S13/4454—Monopulse radar, i.e. simultaneous lobing phase comparisons monopulse, i.e. comparing the echo signals received by an interferometric antenna arrangement
Abstract
Description
This invention disclosure is related to Government contract F3361502D1116 awarded by the Department of the Air Force. The Government has certain rights in this invention.
Phase comparison monopulse angle estimation is a well known technique for measuring angle of arrival of a signal in a radar or other radio frequency electromagnetic sensor. To use this technique, the receiving antenna is typically divided into two halves. The angle of arrival is a function of the ratio of the difference signal (created by subtracting the signal from the two halves) divided by the sum signal (created by adding the two halves). This value is known as the monopulse discriminant.
Generally, the algorithm that performs the angle estimation using the monopulse discriminant relies on the assumption that the value of the monopulse discriminant does not substantially vary as a function of the frequencies that make up the signal. However, this assumption does not hold true for wideband or spread spectrum waveforms or signals when they are measured by an electronically scanned phased array antenna.
Embodiments of the present invention are directed to systems and methods for computing a monopulse discriminant that is substantially frequency invariant even for phase steered antennas when wideband waveforms are used. This frequency invariant monopulse discriminant can be used to compute the angle of arrival of wideband signals.
According to one embodiment of the present invention, a method for estimating a target angle of a wideband signal received on an electronically steered antenna array includes: generating spatial frequency data from the received wideband signal; stabilizing the spatial frequency data to a beam steering direction; compressing the stabilized spatial frequency data to a plurality of frequency range bins; calculating a monopulse discriminant from the stabilized spatial frequency data; and calculating the target angle using the monopulse discriminant.
According to another embodiment of the present invention, a system for stabilizing wideband spatial frequency data for estimating a target angle of a wideband signal on an electronically steered antenna array includes: a spatial frequency processor for transforming the wideband signal to spatial frequency data; a signal stabilizer configured to stabilize the spatial frequency data; a frequency to range transformer configured to compress the stabilized spatial frequency data into a plurality of frequency range bins; a monopulse discriminant calculator for calculating a monopulse discriminant from the compressed stabilized spatial frequency data; and a target angle calculator configured to calculate the target angle using the monopulse discriminant.
According to another embodiment of the present invention, a wideband monopulse radar system includes: an antenna array comprising a plurality of antennas for receiving a wideband monopulse signal; a signal processor for estimating a target angle of the wideband monopulse signal, the signal processor being configured to: transform the wideband monopulse signal to wideband spatial frequency data, stabilize spatial frequency data of the wideband monopulse signal to a beam steering direction; compress the stabilized spatial frequency data to a plurality of frequency range bins; calculate a monopulse discriminant from the compressed stabilized spatial frequency data; and calculate the target angle using the monopulse discriminant.
The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.
According to one embodiment of the present invention, phase comparison monopulse angle estimation may be used in a radar system 100 such as one shown in block diagram form in
Angle estimation of radar returns is often done with an antenna having two channels: a sum channel and a difference channel. The angle of arrival of a received signal (or, equivalently, due to antenna reciprocity theorem, the transmission angle of an outgoing signal) is computed using the sum and difference channels, but the relationship between the angle of arrival and the relative amplitude of the received signal depends on the frequency of the signal when the antenna is steered using adjustment of phase between the elements. As a result, these angle estimation techniques are generally used with narrow band signals rather than wide band signals because there is not a well defined mapping between angle and relative amplitude of the signal for wide band signal. That is, the wide band signals have a range of frequencies, making it difficult to calculate a single angle of arrival for all of the frequencies. Therefore, a substantially frequency independent method of determining the angle of arrival would be useful.
To illustrate the problem, consider a simplified antenna model in which the antenna consists only of two omnidirectional elements spaced along a length L in the x direction. Suppose that a sinusoidal signal s having a frequency ω is incident on the antenna with angle of incidence θ. The signals (s_{0 }and s_{1}) on the two halves of the antenna will be:
Therefore, the sum (s_{Σ}) of the two signals is:
Similarly, the difference (s_{Δ}) of the two signals is:
Therefore, the monopulse discriminant (s_{Δ}/s_{Σ}) is:
Note that this expression can be used to determine the angle of arrival θ from the monopulse discriminant (s_{Δ}/s_{Σ}) as long as
Note also that the relationship depends on the frequency of the signal (ω). If this condition is not satisfied, then the relationship between the monopulse discriminant and angle of arrival admits multiple solutions, which means that the angle of arrival may be ambiguous.
Electronic steering can be used to determine the angle of arrival for signals that do not satisfy the condition
This is done by applying a phase (e.g.,
to each element. That is:
When these channels are combined, they form a monopulse discriminant that looks like:
Similarly, the electronically steered array can be used to determine the angle of arrival for signals satisfying the condition
and therefore θ satisfies the condition:
Therefore, the angle of arrival is centered on:
In other words, the nominal look direction of the array (also referred to as a “steering angle” or “steering direction”) is equal to θ_{look}, which depends on the frequency ω. Using the above described method to determine the angle of arrival is simple for single frequency or narrow band signals because there is little or no variation in frequency ω such that there is little or no variation in the computed direction θ_{look}.
However, using the above described method to compute the angle of arrival of a wide band signal can be difficult because the abovedeveloped monopulse discriminant is frequency dependent and a wide band signal includes a wide range of frequencies.
Assume, for example, a wide band signal incident on an antenna array that is steered to 60 degrees away from boresight. Assume there are sixteen receiving elements in the array with unity spacing see
For a signal at the center spatial frequency, the half power width of the beam in direction cosine space is approximately 1/16
where L=16 is the length of the array and λ=2 as twice the array spacing) The maximum width of the beam at a given steering angle θ_{look }is given by
which can be derived as follows:
For example, at a steering angle of 60 degrees (i.e., direction cosine of about 0.86), this translates to δθ less than about 7.2 degrees, that is, the beam width is about 7.2 degrees.
The maximum deviation of the beam ∂θ_{look }due to frequency can be computed as follows:
For example, if the bandwidth to be collected is equal to 20 percent of the center frequency
then, at a steering angle of 60 degrees (θ_{look}=60°), the maximum deviation of the beam ∂θ_{look }due to frequency variation will be about 19.8 degrees. Therefore, under these example conditions, the deviation of the beam across the frequency is comparable to or larger than the width of the beam (about 7.2 degrees to one side).
For example, as can be seen in the impulse response of the sum channel in
However, it is possible to combine the sum and difference channels in such a way that the impulse responses have the same shape for both the effective sum and difference channels. That is, it is possible to generate sum channels such that the impulse responses are substantially constant across the angles to the targets and to generate difference channels. In addition, this also means that it is possible for the monopulse discriminant to be used for accurate calculation of a target direction.
Embodiments of the present invention are directed toward methods and systems for accurately estimating the angle of arrival of a wide band signal. The methods and systems use signal processing to synthesize the sum and difference channels to provide a single mapping between angle and relative amplitude for all frequencies by creating a linear combination of the original channels and using combination coefficients that depend on frequency.
According to one embodiment of the present invention, conditions are imposed on the monopulse discriminant so that it is independent of frequency (for the sake of convenience, referred to hereafter as a “monopulse discriminant”). Those conditions are:
1. The monopulse discriminant is zero in the look direction for all frequencies.
2. The slope of the monopulse discriminant is frequency independent.
3. The value of the sum channel is normalized to the center frequency.
4. The value of the derivative of the difference channel is normalized to the center frequency.
In addition, the following assumptions will be made in the method:
1. The far field antenna patterns can be represented or approximated by a sum of discrete radiating elements. For a point in space defined by (x, y, z), the complex signal amplitude s given by:
is the spatial frequency, d_{x,yn }are the antenna element locations, w is the element amplitudes (or weights), R=√{square root over (x^{2}+y^{2}+z^{2})} is the range, and φ_{sn }is the steering phase. Note we have assumed a planar antenna located at z=0, which simplifies the calculation, but this assumption is not required for the method.
2. The steering phase corresponds to a particular direction and center frequency so:
are the pointing direction cosines, and
is we nominal spatial frequency corresponding to the radio frequency carrier.
3. The monopulse discriminant can be represented as a ratio of effective antenna channels that are formed from a frequency dependent linear combination of the basic sum and difference channels.
The equations that define the combination depend on frequency
The first condition that the discriminant be zero can be written: s_{Δx}(x_{o},y_{o},z_{o},k)=0, where s_{Δx }is the stabilized difference channel in the x direction. Expressing the unstabilized channels in terms of aperture weights:
where s′_{Δx }is the unstabilized difference channel and s′_{Σx }is the unstabilized sum channel.
A set of coefficients m_{ΔΔx}(k), m_{ΔΣx}(k) can be used to satisfy the condition on s_{Δx}, where these coefficients satisfy:
m _{ΔΔx} s′ _{Δx}(x _{o} ,y _{o} ,z _{o} ,k)+m _{ΔΣx} s′ _{Σx}(x _{o} ,y _{o} ,z _{o} ,k)=s _{Δx}(x _{o} ,y _{o} ,z _{o} ,k)=0
this implies that:
The second condition that the slope of the monopulse discriminant be independent of frequency can be written:
where K_{m }is the slope of the discriminant at the carrier frequency, k_{o},
Recalling now that the first condition is s_{Δx}(x_{o},y_{o},z_{o},k)=0, the two above expressions can be simplified such that:
and similarly,
To satisfy the above constraint that Km be constant as a function of frequency is the constraint we add an additional set of coefficients m_{ΣΔx}(k), m_{ΣΣx}(k) that can be used to form the stabilized sum channel. These coefficients satisfy:
m _{ΣΔx} s′ _{Δx}(x _{o} ,y _{o} ,z _{o} ,k)+m _{ΣΣx} s′ _{Σx}(x _{o} ,y _{o} ,z _{o} ,k)=s _{Σx}(x _{o} ,y _{o} ,z _{o} ,k)
The derivatives of the unstabilized patterns can be expressed in terms of the aperture weights:
This provides a condition on the additional coefficients that can be expressed as a sum over aperture weights:
where, to simplify notation, s′_{Σ} defined as:
with similar definitions for the difference channel and its derivative.
So far, four coefficients have been defined above, but only two equations (1) and (2) link them. The equations for the coefficients can be closed by considering the normalization conditions:
Note that the normalization conditions make the monopulse discriminant condition redundant. This means that an additional condition is needed to solve for the coefficients. This additional condition is that the peak of the sum channel is invariant with respect to spatial frequency. This can be expressed as:
m _{ΣΔ} ∂s′ _{Δ} +m _{ΣΣ} ∂s′ _{Σ}=0 (5)
Solving these equations provides the following expressions for the coefficients:
According to one embodiment of the present invention, the above computed coefficients would then be applied to the unstabilized difference and sum channels to generate stabilized difference and sum channels. For example, the stabilized difference and sum channels would be expressed as s_{Δ}=m_{ΔΔ}s′_{Δ}+m_{ΔΣ}s′_{Σ} and s_{Σ}=m_{ΣΔ}s′_{Δ}+m_{ΣΣ}s′_{Σ}, respectively. A method for performing this stabilization is described in further detail below.
In such an arrangement, most of the energy corresponding to a given target is in just one range bin, so the angle corresponding to the range to the target is an excellent measurement. Furthermore, when there are multiple targets in the set of range bins, the computation would produce an angle to each target.
According to one embodiment of the present invention, the method described in
According to one embodiment of the present invention, a benefit of beam stabilization is realized when the spatial frequency is converted to an impulse response.
Therefore, as can be seen from the above example, embodiments of the present invention provide systems and methods by which a wide band monopulse signal is be stabilized such that it is substantially frequency independent, thereby simplifying and improving the accuracy of the calculation of a target angle from the wide band monopulse signal.
While the present invention has been described in reference to certain exemplary embodiments, it is to be understood to those skilled in the art that the invention is not limited to the disclosed embodiment, but, on the contrary, is intended to cover various modifications included within the spirit and scope of the appended claims and equivalents thereof.
For example, individual hardware components (such as those shown in the embodiments depicted in
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US9368880B2 (en) *  20121116  20160614  Alcatel Lucent  Multisector antenna structure 
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US10122426B2 (en) *  20150720  20181106  Centre Of Excellence In Wireless Technology  Method for beam steering in multipleinput multipleoutput system 
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